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Algebra I Vocabulary Word Wall Cards
Algebra I Vocabulary CardsTable of Contents
Virginia Department of Education, 2014 Algebra I Vocabulary CardsPage 2Expressions and OperationsNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal NumbersAbsolute ValueOrder of OperationsExpressionVariableCoefficientTermScientific NotationExponential FormNegative ExponentZero ExponentProduct of Powers PropertyPower of a Power PropertyPower of a Product PropertyQuotient of Powers PropertyPower of a Quotient PropertyPolynomialDegree of PolynomialLeading CoefficientAdd Polynomials (group like terms)Add Polynomials (align like terms)Subtract Polynomials (group like terms)Subtract Polynomials (align like terms)Multiply PolynomialsMultiply BinomialsMultiply Binomials (model)Multiply Binomials (graphic organizer)Multiply Binomials (squaring a binomial)Multiply Binomials (sum and difference)Factors of a MonomialFactoring (greatest common factor)Factoring (perfect square trinomials)Factoring (difference of squares)Difference of Squares (model)Divide Polynomials (monomial divisor)Divide Polynomials (binomial divisor)Prime PolynomialSquare RootCube RootProduct Property of RadicalsQuotient Property of RadicalsZero Product PropertySolutions or RootsZeros x-Intercepts
Equations and InequalitiesCoordinate PlaneLinear EquationLinear Equation (standard form)Literal EquationVertical LineHorizontal LineQuadratic EquationQuadratic Equation (solve by factoring)Quadratic Equation (solve by graphing)Quadratic Equation (number of solutions)Identity Property of AdditionInverse Property of AdditionCommutative Property of AdditionAssociative Property of AdditionIdentity Property of MultiplicationInverse Property of MultiplicationCommutative Property of MultiplicationAssociative Property of MultiplicationDistributive PropertyDistributive Property (model)Multiplicative Property of ZeroSubstitution PropertyReflexive Property of EqualitySymmetric Property of EqualityTransitive Property of EqualityInequalityGraph of an InequalityTransitive Property for InequalityAddition/Subtraction Property of InequalityMultiplication Property of InequalityDivision Property of InequalityLinear Equation (slope intercept form)Linear Equation (point-slope form)SlopeSlope FormulaSlopes of LinesPerpendicular LinesParallel LinesMathematical NotationSystem of Linear Equations (graphing)System of Linear Equations (substitution)System of Linear Equations (elimination)System of Linear Equations (number of solutions)Graphing Linear InequalitiesSystem of Linear InequalitiesDependent and Independent VariableDependent and Independent Variable (application)Graph of a Quadratic EquationQuadratic Formula
Relations and FunctionsRelations (examples)Functions (examples)Function (definition)DomainRangeFunction NotationParent Functions Linear, QuadraticTransformations of Parent Functions Translation Reflection DilationLinear Function (transformational graphing) Translation Dilation (m>0) Dilation/reflection (m0) Dilation/reflection (a ba + c > b + c
a ba + c b + c
a < ba + c < b + c
a ba + c b + c
Example:d 1.9 -8.7d 1.9 + 1.9 -8.7 + 1.9d -6.8Multiplication Property of Inequality
IfCaseThen
a < bc > 0, positiveac < bc
a > bc > 0, positiveac > bc
a < bc < 0, negativeac > bc
a > bc < 0, negativeac < bc
Example: if c = -25 > -35(-2) < -3(-2) -10 < 6
Division Property of InequalityIfCaseThen
a < bc > 0, positive <
a > bc > 0, positive >
a < bc < 0, negative >
a > bc < 0, negative <
Example: if c = -4-90 -4t 22.5 tLinear Equation: Slope-Intercept Formy = mx + b(slope is m and y-intercept is b)
Example: y = x + 5 ((0,5)-43) (m = b = 5)
Linear Equation: Point-Slope Form
y y1 = m(x x1)where m is the slope and (x1,y1) is the point
Example: Write an equation for the line that passes through the point (-4,1) and has a slope of 2.y 1 = 2(x -4)y 1 = 2(x + 4)y = 2x + 9
Slope
A number that represents the rate of change in y for a unit change in x
(Slope = ) (32)
The slope indicates the steepness of a line.
Slope Formula
The ratio of vertical change tohorizontal change (AB(x1, y1)(x2, y2)x2 x1y2 y1 xy)
slope = m =
Slopes of Lines (Line phas a positive slope.Line n has a negative slope.Vertical line s has an undefined slope.Horizontal line t has a zero slope.)
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1. (Example: The slope of line n = -2. The slope of line p = .-2 = -1, therefore, n is perpendicular to p.)
Parallel Lines
Lines in the same plane that do not intersect are parallel. (yxba)Parallel lines have the same slopes.
(Example: The slope of line a = -2. The slope of line b = -2.-2 = -2, therefore, a is parallel to b.)
Mathematical Notation
Set BuilderNotationReadOther Notation
{x|0 < x 3}The set of all x such that x is greater than or equal to 0 and x is less than 3.0 < x 3
(0, 3]
{y: y -5}The set of all y such that y is greater than or equal to -5.y -5
[-5, )
System of Linear Equations
Solve by graphing:-x + 2y = 32x + y = 4
(The solution, (1, 2), is the only ordered pair that satisfies both equations (the point of intersection).)
System of Linear Equations
Solve by substitution:x + 4y = 17y = x 2
Substitute x 2 for y in the first equation.x + 4(x 2) = 17x = 5Now substitute 5 for x in the second equation.y = 5 2y = 3The solution to the linear system is (5, 3),the ordered pair that satisfies both equations.System of Linear EquationsSolve by elimination:-5x 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable. -5x 6y = 8+ 5x + 2y = 4 -4y = 12 y = -3Now substitute -3 for y in either original equation to find the value of x, the eliminated variable.-5x 6(-3) = 8 x = 2The solution to the linear system is (2,-3), the ordered pair that satisfies both equations.System of Linear EquationsIdentifying the Number of SolutionsNumber of SolutionsSlopes and y-intercepts (xy)Graph
One solutionDifferent slopes (xy)
No solutionSame slope anddifferent y-intercepts (xy)
Infinitely many solutionsSame slope andsame y-intercepts
Graphing Linear InequalitiesExampleGraph
y x + 2 (y) (x)
y > -x 1 (y) (x)
System of Linear Inequalities
Solve by graphing:y x 3 (y)y -2x + 3 (The solution region contains all ordered pairs that are solutions to both inequalities in the system.(-1,1) is one solution to the system located in the solution region.)
(x)
Dependent andIndependent Variable
x, independent variable(input values or domain set)
Example:y = 2x + 7
y, dependent variable(output values or range set)
Dependent andIndependent Variable
Determine the distance a car will travel going 55 mph.hd
00
155
2110
3165
d = 55h (dependent) (independent)
Graph of a Quadratic Equationy = ax2 + bx + ca 0 (y)Example: y = x2 + 2x 3
(line of symmetry) (x) (vertex)The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex.Quadratic Formula
Used to find the solutions to any quadratic equation of the form, y = ax2 + bx + c
x =
RelationsRepresentations of relationships
xy
-34
00
1-6
22
5 (Example 2)-1
(Example 1){(0,4), (0,3), (0,2), (0,1)} (Example 3)FunctionsRepresentations of functions
xy
32
24
02
-12
(Example 4) (Example 3) (Example 2) (Example 1) (x) (y) ({(-3,4), (0,3), (1,2), (4,6)})Function
A relationship between two quantities in which every input corresponds to exactly one output (x) (y) (246810) (10753)
A relation is a function if and only if each element in the domain is paired with a unique element of the range.
Domain
A set of input values of a relation
Examples:inputoutput
xg(x)
-20
-11
02
13
(f(x))
(x) (The domain of g(x) is {-2, -1, 0, 1}.) (The domain of f(x) is all real numbers.)Range
A set of output values of a relation
(f(x))Examples:inputoutput
xg(x)
-20
-11
02
13
(x) (The range of f(x) is all real numbers greater than or equal to zero.) (The range of g(x) is {0, 1, 2, 3}.)
Function Notation
f(x)
f(x) is read the value of f at x or f of x
Example:f(x) = -3x + 5, find f(2).f(2) = -3(2) + 5f(2) = -6
Letters other than f can be used to name functions, e.g., g(x) and h(x)
Parent Functions (y)Linear (x) f(x) = x
(y) Quadratic f(x) = x2 (x)
Transformations of Parent Functions
Parent functions can be transformed to create other members in a family of graphs.
Translationsg(x) = f(x) + kis the graph of f(x) translated vertically k units up when k > 0.
k units down when k < 0.
g(x) = f(x h)is the graph of f(x) translated horizontally h units right when h > 0.
h units left when h < 0.
Transformations of Parent Functions
Parent functions can be transformed to create other members in a family of graphs.
Reflectionsg(x) = -f(x)is the graph of f(x) reflected over the x-axis.
g(x) = f(-x)is the graph of f(x) reflected over the y-axis.
Transformations of Parent Functions
Parent functions can be transformed to create other members in a family of graphs.
Dilationsg(x) = a f(x)is the graph of f(x) vertical dilation (stretch) if a > 1.
vertical dilation (compression) if 0 < a < 1.
g(x) = f(ax)is the graph of f(x) horizontal dilation (compression) if a > 1.
horizontal dilation (stretch) if 0 < a < 1.
Transformational GraphingLinear functionsg(x) = x + b (y) (Examples:f(x) = xt(x) = x + 4h(x) = x 2 )
(x)
Vertical translation of the parent function, f(x) = xTransformational GraphingLinear functionsg(x) = mx (y)m>0 (Examples:f(x) = xt(x) = 2xh(x) = x) (x)
Vertical dilation (stretch or compression) of the parent function, f(x) = x Transformational GraphingLinear functionsg(x) = mx (y)m < 0 (Examples:f(x) = xt(x) = -xh(x) = -3xd(x) = -x) (x)
Vertical dilation (stretch or compression) with a reflection of f(x) = x Transformational GraphingQuadratic functionsh(x) = x2 + c (y) (x) (Examples:f(x) = x2g(x) = x2 + 2t(x) = x2 3)
Vertical translation of f(x) = x2Transformational GraphingQuadratic functionsh(x) = ax2 (y)a > 0
(x) (Examples: f(x) = x2 g(x) = 2x2 t(x) = x2)
Vertical dilation (stretch or compression) of f(x) = x2Transformational GraphingQuadratic functionsh(x) = ax2 (y)a < 0 (Examples: f(x) = x2 g(x) = -2x2 t(x) = x2)
(x)
Vertical dilation (stretch or compression) with a reflection of f(x) = x2Transformational GraphingQuadratic functions h(x) = (x + c)2 (y) (Examples:f(x) = x2g(x) = (x + 2)2t(x) = (x 3)2)
(x)Horizontal translation of f(x) = x2
Direct Variationy = kx or k = constant of variation, k 0 (y)Example: y = 3x or 3 =
(x)
The graph of all points describing a direct variation is a line passing through the origin.Inverse Variationy = or k = xyconstant of variation, k 0 (y) Example: y = or xy = 3 (x)
The graph of all points describing an inverse variation relationship are 2 curves that are reflections of each other.
Statistics Notation
th element in a data set
mean of the data set
variance of the data set
standard deviation of the data set
number of elements in the data set
Mean
A measure of central tendency
Example: Find the mean of the given data set.Data set: 0, 2, 3, 7, 8
Balance Point (44231 0 1 2 3 4 5 6 7 8)
Numerical Average
Median
A measure of central tendency
Examples: Find the median of the given data sets.
Data set: 6, 7, 8, 9, 9
The median is 8.
Data set: 5, 6, 8, 9, 11, 12
The median is 8.5.
Mode
Data SetsMode
3, 4, 6, 6, 6, 6, 10, 11, 146
0, 3, 4, 5, 6, 7, 9, 10none
5.2, 5.2, 5.2, 5.6, 5.8, 5.9, 6.05.2
1, 1, 2, 5, 6, 7, 7, 9, 11, 121, 7bimodal
A measure of central tendency
Examples:
Box-and-Whisker Plot
A graphical representation of the five-number summary
(LowerQuartile (Q1)LowerExtremeUpperQuartile (Q3)UpperExtremeMedianInterquartile Range (IQR)5101520)
(A1, A2, AFDA)Summation (stopping pointupper limit)
(summation sign) (typical element)
(index of summation) (starting pointlower limit)
This expression means sum the values of x, starting at x1 and ending at xn.
(= x1 + x2 + x3 + + xn)
Example: Given the data set {3, 4, 5, 5, 10, 17}
Mean Absolute Deviation
A measure of the spread of a data set
Mean Absolute Deviation
=
The mean of the sum of the absolute value of the differences between each element and the mean of the data set
VarianceA measure of the spread of a data set
The mean of the squares of the differences between each element and the mean of the data set
Standard Deviation
A measure of the spread of a data set
The square root of the mean of the squares of the differences between each element and the mean of the data set or the square root of the variance
z-Score
The number of standard deviations an element is away from the mean
where x is an element of the data set, is the mean of the data set, and is the standard deviation of the data set.
Example: Data set A has a mean of 83 and a standard deviation of 9.74. What is the zscore for the element 91 in data set A? z = = 0.821
z-Score
The number of standard deviations an element is from the mean
(z = 1z = 2z = 3z = -1z = -2z = -3z = 0)
(Mean) (X) (X) (Elements within one standard deviation of the mean) (X) (X) (X) (X) (X) (X) (X) (X) (X) (5101520) (X) (X) (X) (X) (X) (X) (X) (X) (X) (X) (X) (X) (X)Elements within One Standard Deviation ()of the Mean ()Scatterplot
Graphical representation of the relationship between two numerical sets of data (xy)
Positive Correlation
In general, a relationship where the dependent (y) values increase as independent values (x) increase (xy)
Negative Correlation
In general, a relationship where the dependent (y) values decrease as independent (x) values increase. (xy)
No Correlation
No relationship between the dependent (y) values and independent (x) values. (xy)
Curve of Best Fit
(Calories and Fat Content)
Outlier Data
(Outlier) (Miles per GallonFrequencyGas Mileage for Gasoline-fueled CarsOutlier)-2-101234-7-5-3-1135-4-4-4-4-4-4-4-3-2-10123-3-2-101236666666-2-1012310.50-0.5-1-1.5-2-10123-5-3-1135y1-3-2-101231234567y2-3-2-10123-2.3333333333333335-1.3333333333333335-0.333333333333333370.666666666666666631.66666666666666652.66666666666666653.6666666666666665-2-1012210-1-2y-5-4-3-2-101231250-3-4-30512yy-3-2-101239410149yy-3-2-101239410149-3-2-10123-3-2-10123yy-3-2-101239410149-3-2-10123-3-2-10123-3-2-101231234567-3-2-10123-5-4-3-2-101y-3-2-10123-3-2-10123y1-3-2-10123-6-4-20246y2-3-2-10123-1.5-1-0.500.511.5-3-2-101239410149-3-2-10123116323611-3-2-1012361-2-3-216-4-3-2-1012349410149-4-3-2-10123482028-4-3-2-1012345.333333333333393431.33333333333333330.3333333333333333100.333333333333333311.333333333333333335.3333333333333934-4-3-2-1012349410149-4-3-2-101234-8-20-2-8-4-3-2-101234-5.3333333333333934-3-1.3333333333333333-0.333333333333333310-0.33333333333333331-1.3333333333333333-3-5.3333333333333934-3-2-101239410149-5-4-3-2-101941014901234569410149-2-1012-6-3036-5-4-3-2-1-0.50.512345-0.60000000000000064-0.7500000000000111-1-1.5-3-6631.510.75000000000001110.60000000000000064Wingspan vs. HeightHeight (in.)484746524351535347444149484647535454465151.5595856494748504251526948434448.548.546.550535255485150605957Height (in.)Wingspan (in.)4520587320==++++=mnxnii=-1m